"Do you drink juice and milk?"
Translation:Ви п'єте сік і молоко?
The apostrophe is acting like a ъ (твёрдый знак). And, no, the explanation is rather simple: it is just how Ukrainian works.
Apparently, all labial consonants (м, б, п, в, ф) almost require this "hard sign" before я, ї, є, ю (except when they are preceded by a voiced consonant inside the root; doesn't work if it is a prefix ending in a voice consonant), and р (in certain cases). There are rules that you may read up later :).